Combinatorics in (2,1)-categories
Category Theory
2025-05-08 v3 Combinatorics
Abstract
Groupoid cardinality is an invariant of locally finite groupoids which has many of the properties of the cardinality of finite sets, but which takes values in all non-negative real numbers, and accounts for the morphisms of a groupoid. Several results on groupoid cardinality are proved, analogous to the relationship between cardinality of finite sets and i.e. injective or surjective functions. We also generalize to a broad class of (2,1)-categories a famous theorem of Lov\'asz which characterizes the isomorphism type of relational structures by counting the number of homomorphisms into them.
Cite
@article{arxiv.2502.03585,
title = {Combinatorics in (2,1)-categories},
author = {Krista Zehr},
journal= {arXiv preprint arXiv:2502.03585},
year = {2025}
}